POJ 1163 The Triangle(入门动规）

The Triangle

Time Limit: 1000MS		Memory Limit: 10000K
Total Submissions: 49860		Accepted: 30112

Description

7
3   8
8   1   0
2   7   4   4
4   5   2   6   5

(Figure 1)

Figure 1 shows a number triangle. Write a program that calculates the highest sum of numbers passed on a route that starts at the top and ends somewhere on the base. Each step can go either diagonally down to
the left or diagonally down to the right. 

Input

Your program is to read from standard input. The first line contains one integer N: the number of rows in the triangle. The following N lines describe the data of the triangle. The number of rows in the triangle
is > 1 but <= 100. The numbers in the triangle, all integers, are between 0 and 99.
Output

Your program is to write to standard output. The highest sum is written as an integer.
Sample Input

5
7
3 8
8 1 0
2 7 4 4
4 5 2 6 5

Sample Output

30

Source

IOI 1994

状态转移方程：dp[i][j]=max(dp[i][j],max(dp[i-1][j-1],dp[i-1][j])+f[i][j]);

dp[i][j]表示在第i行第j列可以到达的最大值。

AC代码

#include<iostream>
#include<cstdio>
using namespace std;
int f[105][105];
int dp[105][105];
int main(){
int n;
scanf("%d",&n);
for(int i=1;i<=n;i++){
for(int j=1;j<=i;j++){
scanf("%d",&f[i][j]);
}
}
for(int i=1;i<=n;i++){
for(int j=1;j<=i;j++){
if(dp[i][j]==0)dp[i][j]=f[i][j];
dp[i][j]=max(dp[i][j],max(dp[i-1][j-1],dp[i-1][j])+f[i][j]);
}
}
int ans=0;
for(int i=1;i<=n;i++){
ans=max(ans,dp
[i]);
}
printf("%d\n",ans);
return 0;
}